There is a well-documented custom that a father wears a Tallit – and recites the Beracha of "Le’hit’atef Be’sisit" – at his son’s Berit Mila. This custom is mentioned by the Kaf Ha’haim (Orah Haim 25:96). When it comes to wearing Tefillin, however, we find divergent customs. The practice of Ashkenazim is that the father wears Tefillin at a Berit Mila; he either keeps his Tefillin on, if the Berit takes place immediately after Shaharit, or, if the Berit takes place later, he puts the Tefillin on again, with a Beracha.
Among Sepharadim, however, the preferred custom is not to wear Tefillin at a Berit. As noted by the Hid"a (Rav Haim Yosef David Azulai, 1724-1807), in his work Mar’it Ha’ayin, Tefillin has the status of an "Ot" (a sign of our covenant with God), and Berit Mila is likewise considered an "Ot." By wearing Tefillin at a Berit Mila, one appears as though he belittles the Berit’s status as an "Ot." Thus, the Hid"a writes, just as we do not wear Tefillin on Shabbat, because Shabbat is considered an "Ot," one should also not wear Tefillin at a Berit Mila. Accordingly, Hacham Ovadia Yosef, both in Yabia Omer (vol. 3, p. 13) and in Soba Semahot (7:2), rules that Tefillin should preferably not be worn at a Berit Mila. This was also the position of Hacham Baruch Ben-Haim, who noted that there is often a lot of mingling that takes place just prior to a Berit, and it is thus inappropriate to wear Tefillin, which requires focus and concentration.
Nevertheless, one should not object to those who wear Tefillin at a Berit, even among Sepharadim, because there are documented accounts of great Sephardic Sages who followed the practice of wearing Tefillin. It is reported, for example, that Hacham Ben Sion Abba Shaul (Israel, 1923-1998) put on Tefillin when he served as Sandak for his grandson, and the great Sadik Hacham Mansur Ben Shimon also wore Tefillin at Beritot. Therefore, notwithstanding the ruling of Hacham Ovadia, those who have a family tradition to wear Tefillin at a Berit may do so, and others should not object.
According to all opinions, however, if a Berit Mila takes place on Rosh Hodesh, when the Tefillin is removed before Musaf, one should not put the Tefillin on again after the prayer service for the Berit. Since the Tefillin is removed before Musaf, it should not be worn again afterward for the Berit, according to all views. This point is made by the Kaf Ha’haim (ibid.) as well as by Hacham Ovadia Yosef, in Yabia Omer (ibid.).
Finally, Hacham Ovadia adds that it is proper for the father to recite before the Berit the special prayer composed by the Hid"a for this occasion, which appears in his work Abodat Ha’kodesh and is also printed in some editions of the Siddur.
Summary: The custom among Ashkenazim is that a father wears Tefillin during his son’s Berit Mila, but Sepharadim should not wear Tefillin at a Berit unless one has a family tradition to do so. It is proper for the father to recite before the Berit the special prayer composed by the Hid"a for this occasion, which is printed in some editions of the Siddur.
